Quantitative Applications - Titrations Based on Redox Reactions

Quantitative Applications

As with acid–base and complexation titrations, redox titrations are not frequently used in modern analytical laboratories. Nevertheless, several important applications continue to find favor in environmental, pharmaceutical, and industrial laborato- ries. In this section we review the general application of redox titrimetry. We begin, however, with a brief discussion of selecting and characterizing redox titrants, and methods for controlling the analyte’s oxidation state.

Adjusting the Analyte’s Oxidation State 

If a redox titration is to be used in a quantitative analysis, the analyte must initially be present in a single oxidation state. For example, the iron content of a sample can be determined by a redox titration in which Ce4+ oxidizes Fe2+ to Fe3+. The process of preparing the sample for analysis must ensure that all iron is present as Fe2+. Depending on the sample and the method of sample preparation, however, the iron may initially be present in both the +2 and +3 oxidation states. Before titrating, any Fe3+ that is present must be re- duced to Fe2+. This type of pretreatment can be accomplished with an auxiliary re- ducing or oxidizing agent.

Metals that are easily oxidized, such as Zn, Al, and Ag, can serve as auxiliary re- ducing agents. The metal, as a coiled wire or powder, is placed directly in the solu- tion where it reduces the analyte. Of course any unreacted auxiliary reducing agent will interfere with the analysis by reacting with the titrant. The residual auxiliary re- ducing agent, therefore, must be removed once the analyte is completely reduced. This can be accomplished by simply removing the coiled wire or by filtering.

An alternative approach to using an auxiliary reducing agent is to immobilize it in a column. To prepare a reduction column, an aqueous slurry of the finely divided metal is packed in a glass tube equipped with a porous plug at the bottom (Figure 9.39). The sample is placed at the top of the column and moves through the column under the influence of gravity or vacuum suction. The length of the reduction col- umn and the flow rate are selected to ensure the analyte’s complete reduction.

Two common reduction columns are used. In the Jones reductor the column is filled with amalgamated Zn prepared by briefly placing Zn granules in a solution of HgCl₂ to form Zn(Hg). Oxidation of the amalgamated Zn

Zn(Hg)(s) < = = = = >  Zn2+(aq) + Hg(l)+ 2e–

provides the electrons for reducing the analyte. In the Walden reductor the column is filled with granular Ag metal. The solution containing the analyte is acidified with HCl and passed through the column where the oxidation of Ag

Ag(s)+ Cl–(aq)< == == > AgCl(s)+ e–

provides the necessary electrons for reducing the analyte. Examples of both reduc- tion columns are shown in Table 9.19.

Several reagents are commonly used as auxiliary oxidizing agents, including ammonium peroxydisulfate, (NH₄)₂S₂O₈, and hydrogen peroxide, H₂O₂. Ammo- nium peroxydisulfate is a powerful oxidizing agent

S₂O 2–(aq)+ 2e– < == == >  2SO₄2–(aq)

capable of oxidizing Mn2+ to MnO₄–, Cr3+ to Cr₂O₄2–, and Ce3+ to Ce4+. Excess per- oxydisulfate is easily destroyed by briefly boiling the solution. The reduction of hy- drogen peroxide in acidic solution

H₂O₂(aq)+ 2H₃O+(aq)+ 2e– < = = = = > 4H₂O(l)

provides another method for oxidizing an analyte. Excess H₂O₂ also can be de- stroyed by briefly boiling the solution.

Selecting and Standardizing a Titrant 

In quantitative work the titrant’s concen- tration must remain stable during the analysis. Since titrants in a reduced state are susceptible to air oxidation, most redox titrations are carried out using an oxidizing agent as the titrant. The choice of which of several common oxidizing titrants is best for a particular analysis depends on the ease with which the analyte can be oxidized. Analytes that are strong reducing agents can be successfully titrated with a relatively weak oxidizing titrant, whereas a strong oxidizing titrant is required for the analysis of analytes that are weak reducing agents.

The two strongest oxidizing titrants are MnO₄– and Ce4+, for which the reduc- tion half-reactions are

MnO₄–(aq)+ 8H₃O+(aq)+ 5e– t< =  = = > Mn2+(aq) + 12H₂O(l)

Ce4+(aq)+ e–  <   == == >  Ce3+(aq)

Solutions of Ce4+ are prepared from the primary standard cerium ammonium ni- trate, Ce(NO₃)₄ 2NH₄NO₃, in 1 M H₂SO₄. When prepared from reagent grade materials, such as Ce(OH)₄, the solution must be standardized against a primary standard reducing agent such as Na₂C₂O₄ or Fe2+ (prepared using Fe wire). Ferroin is a suitable indicator when standardizing against Fe2+ (Table 9.20). Despite its availability as a primary standard and its ease of preparation, Ce4+ is not as fre- quently used as MnO₄– because of its greater expense.

Solutions of MnO₄– are prepared from KMnO₄, which is not available as a pri- mary standard. Aqueous solutions of permanganate are thermodynamically unsta- ble due to its ability to oxidize water.

4MnO₄–(aq)+ 2H₂O(l) < == == >  4MnO₂(s)+ 3O₂(g) + 4OH–(aq)

This reaction is catalyzed by the presence of MnO₂, Mn2+, heat, light, and the pres- ence of acids and bases. Moderately stable solutions of permanganate can be pre- pared by boiling for an hour and filtering through a sintered glass filter to remove any solid MnO₂ that precipitates. Solutions prepared in this fashion are stable for 1–2 weeks, although the standardization should be rechecked periodically. Stan- dardization may be accomplished using the same primary standard reducing agents that are used with Ce4+, using the pink color of MnO₄– to signal the end point (Table 9.20).

Potassium dichromate is a relatively strong oxidizing agent whose principal ad- vantages are its availability as a primary standard and the long-term stability of its solutions. It is not, however, as strong an oxidizing agent as MnO₄– or Ce4+, which prevents its application to the analysis of analytes that are weak reducing agents. Its reduction half-reaction is

Cr₂O₇2–(aq) + 14H₃O+(aq)+ 6e– < = = = = > 2Cr3+(aq) + 21H₂O(l)

Although solutions of Cr₂O₇2– are orange and those of Cr3+ are green, neither color is intense enough to serve as a useful indicator. Diphenylamine sulfonic acid, whose oxidized form is purple and reduced form is colorless, gives a very distinct end point signal with Cr₂O₇2–.

Iodine is another commonly encountered oxidizing titrant. In comparison with MnO₄–, Ce4+, and Cr₂O₇2–, it is a weak oxidizing agent and is useful only for the analysis of analytes that are strong reducing agents. This apparent limitation, how- ever, makes I₂ a more selective titrant for the analysis of a strong reducing agent in the presence of weaker reducing agents. The reduction half-reaction for I₂ is

I₂(aq)+ 2e– < = = = = > 2I–(aq)

Because of iodine’s poor solubility, solutions are prepared by adding an excess of I–. The complexation reaction

I₂(aq)+ I–(aq) < = = = = > I₃–(aq)

increases the solubility of I₂ by forming the more soluble triiodide ion, I₃–. Even though iodine is present as I₃– instead of I₂, the number of electrons in the reduc- tion half-reaction is unaffected.

I₃–(aq)+ 2e– < = = = = > 3I–(aq)

Solutions of I₃– are normally standardized against Na₂S₂O₃ (see Table 9.20) using starch as a specific indicator for I₃–.

Oxidizing titrants such as MnO₄–, Ce4+, Cr₂O₇2– and I₃–, are used to titrate ana- lytes that are in a reduced state. When the analyte is in an oxidized state, it can be reduced with an auxiliary reducing agent and titrated with an oxidizing titrant. Al- ternatively, the analyte can be titrated with a suitable reducing titrant. Iodide is a relatively strong reducing agent that potentially could be used for the analysis of an- alytes in higher oxidation states. Unfortunately, solutions of I– cannot be used as a direct titrant because they are subject to the air oxidation of I– to I₃–.

3I–(aq) < = = = = > I₃–(aq)+ 2e–

Instead, an excess of KI is added, reducing the analyte and liberating a stoichiometric amount of I₃–. The amount of I₃– produced is then determined by a back titra- tion using Na₂S₂O₃ as a reducing titrant.

2S₂O 2–(aq) < = = = = > S₄O 2–(aq)+ 2e–

Solutions of Na₂S₂O₃ are prepared from the pentahydrate and must be stan- dardized before use. Standardization is accomplished by dissolving a carefully weighed portion of the primary standard KIO₃ in an acidic solution containing an excess of KI. When acidified, the reaction between IO₃– and I–

IO₃–(aq)+ 8I–(aq)+ 6H₃O+(aq) < == = > 3I₃–(aq)+ 9H O(l)

liberates a stoichiometric amount of I₃–. Titrating I₃– using starch as a visual indica- tor allows the determination of the titrant’s concentration.

Although thiosulfate is one of the few reducing titrants not readily oxidized by contact with air, it is subject to a slow decomposition to bisulfite and ele- mental sulfur. When used over a period of several weeks, a solution of thiosul- fate should be restandardized periodically. Several forms of bacteria are able to metabolize thiosulfate, which also can lead to a change in its concentration. This problem can be minimized by adding a preservative such as HgI₂ to the solution.

Another reducing titrant is ferrous ammonium sulfate, Fe(NH₄)₂(SO₄)₂ 6H₂O, in which iron is present in the +2 oxidation state. Solutions of Fe2+ are normally very susceptible to air oxidation, but when prepared in 0.5 M H₂SO₄ the solution may remain stable for as long as a month. Periodic restandardization with K₂Cr₂O₇ is advisable. The titrant can be used in either a direct titration in which the Fe2+ is oxidized to Fe3+, or an excess of the solution can be added and the quantity of Fe3+ produced determined by a back titration using a standard solution of Ce4+ or Cr₂O 2–.

Inorganic Analysis 

Redox titrimetry has been used for the analysis of a wide range of inorganic analytes. Although many of these methods have been replaced by newer methods, a few continue to be listed as standard methods of analysis. In this section we consider the application of redox titrimetry to several important envi- ronmental, public health, and industrial analyses.

One of the most important applications of redox titrimetry is in evaluating the chlorination of public water supplies. In Method 9.3 an approach for determining the total chlorine residual was described in which the oxidizing power of chlorine is used to oxidize I– to I₃–. The amount of  I₃– formed is determined by a back titration with S₂O₃2–.

The efficiency of chlorination depends on the form of the chlorinating species. For this reason it is important to distinguish between the free chlorine residual, due to Cl₂, HOCl, and OCl–, and the combined chlorine residual. The latter form of chlorine results from the reaction of ammonia with the free chlo- rine residual, forming NH₂Cl, NHCl₂, and NCl₃. When a sample of iodide-free chlorinated water is mixed with an excess of the indicator N,N-diethyl-p- phenylenediamine (DPD), the free chlorine oxidizes a stoichiometric portion of DPD to its red-colored form. The oxidized DPD is then titrated back to its color- less form with ferrous ammonium sulfate, with the volume of titrant being pro- portional to the amount of free residual chlorine. Adding a small amount of KI reduces monochloramine, NH₂Cl, forming I₃–. The I₃– then oxidizes a portion of the DPD to its red-colored form. Titrating the oxidized DPD with ferrous am- monium sulfate yields the amount of NH₂Cl in the sample. The amount of dichloramine and trichloramine are determined in a similar fashion.

The methods described earlier for determining the total, free, or combined chlorine residual also are used in establishing the chlorine demand of a water sup- ply. The chlorine demand is defined as the quantity of chlorine that must be added to a water supply to completely react with any substance that can be oxi- dized by chlorine while also maintaining the desired chlorine residual. It is deter- mined by adding progressively greater amounts of chlorine to a set of samples drawn from the water supply and determining the total, free, or combined chlo- rine residual.

Another important example of redox titrimetry that finds applications in both public health and environmental analyses is the determination of dissolved oxygen. In natural waters the level of dissolved O₂ is important for two reasons: it is the most readily available oxidant for the biological oxidation of inorganic and organic pollutants; and it is necessary for the support of aquatic life. In wastewater treat- ment plants, the control of dissolved O₂ is essential for the aerobic oxidation of waste materials. If the level of dissolved O₂ falls below a critical value, aerobic bacte- ria are replaced by anaerobic bacteria, and the oxidation of organic waste produces undesirable gases such as CH₄ and H₂S.

One standard method for determining the dissolved O₂ content of natural wa- ters and wastewaters is the Winkler method. A sample of water is collected in a fash- ion that prevents its exposure to the atmosphere (which might change the level of dissolved O₂). The sample is then treated with a solution of MnSO₄, and then with a solution of NaOH and KI. Under these alkaline conditions Mn2+ is oxidized to MnO₂ by the dissolved oxygen.

2Mn2+(aq) + 4OH–(aq)+ O₂(aq) → 2MnO₂(s)+ 2H₂O(l)

After the reaction is complete, the solution is acidified with H₂SO₄. Under the now acidic conditions I– is oxidized to I₃– by MnO₂.

MnO₂(s)+ 3I–(aq)+ 4H₃O+(aq) → Mn2+(aq)+I₃–(aq)+ 6H₂O(l)

The amount of I₃– formed is determined by titrating with S₂O₃2– using starch as an indicator. The Winkler method is subject to a variety of interferences, and several modifications to the original procedure have been proposed. For example, NO₂– in- terferes because it can reduce I₃– to I– under acidic conditions. This interference is eliminated by adding sodium azide, NaN₃, reducing NO₂– to N₂. Other reducing agents, such as Fe2+, are eliminated by pretreating the sample with KMnO₄, and de- stroying the excess permanganate with K₂C₂O₄.

Another important example of a redox titration for inorganic analytes, which is important in industrial labs, is the determination of water in nonaqueous solvents. The titrant for this analysis is known as the Karl Fischer reagent and consists of a mixture of iodine, sulfur dioxide, pyridine, and methanol. The concentration of pyridine is sufficiently large so that I₂ and SO₂ are complexed with the pyridine (py) as py I₂ and py SO₂. When added to a sample containing water, I₂ is reduced to I–, and SO₂ is oxidized to SO₃.

py . I₂ + py . SO₂ + py+ H₂O → 2py . HI+ py . SO₃

Methanol is included to prevent the further reaction of py . SO₃ with water. The titration’s end point is signaled when the solution changes from the yellow color of the products to the brown color of the Karl Fischer reagent.

Organic Analysis 

Redox titrimetric methods also are used for the analysis of or- ganic analytes. One important example is the determination of the chemical oxygen demand (COD) in natural waters and wastewaters. The COD provides a measure of the quantity of oxygen necessary to completely oxidize all the organic matter in a sample to CO₂ and H₂O. No attempt is made to correct for organic matter that can- not be decomposed biologically or for which the decomposition kinetics are very slow. Thus, the COD always overestimates a sample’s true oxygen demand. The de- termination of COD is particularly important in managing industrial wastewater treatment facilities where it is used to monitor the release of organic-rich wastes into municipal sewer systems or the environment.

The COD is determined by refluxing the sample in the presence of excess K₂Cr₂O₇, which serves as the oxidizing agent. The solution is acidified with H₂SO₄, and Ag₂SO₄ is added as a catalyst to speed the oxidation of low-molecular-weight fatty acids. Mercuric sulfate, HgSO₄, is added to complex any chloride that is pres- ent, thus preventing the precipitation of the Ag+ catalyst as AgCl. Under these con- ditions, the efficiency for oxidizing organic matter is 95–100%. After refluxing for 2h, the solution is cooled to room temperature, and the excess Cr₂O₇2– is deter- mined by a back titration, using ferrous ammonium sulfate as the titrant and fer- roin as the indicator. Since it is difficult to completely remove all traces of organic matter from the reagents, a blank titration must be performed. The difference in the amount of ferrous ammonium sulfate needed to titrate the blank and the sample is proportional to the COD.

Iodine has been used as an oxidizing titrant for a number of compounds of pharmaceutical interest. Earlier we noted that the reaction of S₂O₃2– with I₃– pro- duces the tetrathionate ion, S₄O₆2–. The tetrathionate ion is actually a dimer consist- ing of two thiosulfate ions connected through a disulfide (-S-S-) linkage. In the same fashion, I₃– can be used to titrate mercaptans of the general formula RSH, forming the dimer RSSR as a product. The amino acid cysteine also can be titrated with I₃–. The product of this titration is cystine, which is a dimer of cysteine. Triio- dide also can be used for the analysis of ascorbic acid (vitamin C) by oxidizing the enediol functional group to an alpha diketone

and for the analysis of reducing sugars, such as glucose, by oxidizing the aldehyde functional group to a carboxylate ion in a basic solution.

Organic compounds containing a hydroxyl, carbonyl, or amine functional group adjacent to a hydoxyl or carbonyl group can be oxidized using metaperio- date, IO₃–, as an oxidizing titrant.

IO₃–(aq)+H O(l)+ 2e– → IO₃–(aq) + 2OH–(aq)

A two-electron oxidation cleaves the C—C bond between the two functional groups, with hydroxyl groups being oxidized to aldehydes or ketones, carbonyl functional groups being oxidized to carboxylic acids, and amines being oxidized to an aldehyde and an amine (ammonia if the original amine was primary). For exam- ple, treatment of serine with IO₃– results in the following oxidation reaction

The analysis is conducted by adding a known excess of IO₃– to the solution contain- ing the analyte and allowing the oxidation to take place for approximately 1 h at room temperature. When the oxidation is complete, an excess of KI is added, which reacts with the unreacted IO₃– to form IO₃– and I₃–.

IO₃–(aq)+ 3I–(aq)+H O(l) → IO₃–(aq)+I₃–(aq) + 2OH–(aq)

he I₃– is then determined by titrating with S₂O₃2– using starch as an indicator.

Quantitative Calculations 

The stoichiometry of a redox reaction is given by the con- servation of electrons between the oxidizing and reducing agents; thus

Example 9.13 shows how this equation is applied to an analysis based on a direct titration.